A numerical study of boundary-layer dynamics in a mountain valley

A higher order closure model is applied to simulate the dynamics in an area with a deep valley characterized by complex terrain in the southwestern US. The simulation results show generally good agreement with measured profiles at two locations within the valley. Both the measurements and the simulations indicate that the flow dynamics in the area are highly influenced by the topography and meandering of the valley, and can be resolved only by the full three-dimensional model code. The wind veering simulated over the range of the topographic elevations is often larger than 100 deg and in some cases as large as 180 deg, as a consequence of topographic forcing. In the case of an infinitely long valley, as is assumed in two-dimensional test simulations, a strong low-level jet occurs within the valley during stable conditions. The jet is mainly a consequence of the Coriolis effect. However, the jet development is significantly reduced due to asymmetric effects of the actual topography treated in the three-dimensional simulations. Tests with the two-dimensional nonhydrostatic version of the model show significant wave responses for a stable stratified flow over the valley. The structure resembles nonlinear mesoscale lee waves, which are intrinsically nonhydrostatic. However, considering the three-dimensional nature of this valley system, a better understanding and verification of the nonhydrostatic effects requires both a three-dimensional nonhydrostatic numerical model and an observational data set which is fully representative in all three dimensions.List of symbols (unless otherwise defined in the text) B ₁ closure constant - f Coriolis parameter - g acceleration of gravity - K _M ,K _H ,K _R turbulent exchange coefficients for momentum, heat and moisture - k von Karman constant - L Monin-Obukhov length - q ² twice the turbulent kinetic energy - R specific humidity - s height of the model top - T _g ground surface temperature - t time - U, V horizontal components of wind - U _g ,V _g geostrophic wind components - u, w perturbation components ofU andW wind components - u _* friction velocity - W vertical wind component in the terrain-following coordinates - x, y horizontal coordinates - Z actual height above sea level - z actual height above ground - z ₀ roughness length - z _g terrain height - z _i depth of the convective boundary layer - ₁ closure constant - coefficient of thermal expansion - height in the terrain-following coordinate - master length scale in the turbulent parameterization - scaled pressure (Exner function) - potential temperature - _m normalized vertical wind shear     

A theoretical explanation of mountain and valley winds by a numerical method

Summary A theoretical model of the local circulation in a valley is obtained. The region under study consists of a V-shaped trough of finite length leading into a flat plain, and a given rate of heat flow from ground to air is assumed. The equations of motion are solved numerically, and give a circulation featuring valley and slope winds, their respective anti-winds (compensating flow at higher levels) and vertical currents.

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Zusammenfassung Es wird ein theoretisches Modell der lokalen Zirkulation in einem Tale entwickelt. Das untersuchte Gebiet ist ein V-förmiges Tal endlicher Länge, das in eine Ebene mündet. Es wird die Annahme zugrunde gelegt, daß eine gegebene Wärmemenge von der Erdoberfläche an die Luft abgegeben wird. Die numerische Lösung der Bewegungsgleichungen gibt die Berg- und Hangwinde sowie die entsprechenden Ausgleichströmungen oder Antiwinde und Vertikalströmungen.

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Résumé Un modèle théorique de l'écoulement local d'une vallée est développé. La région étudiée consiste en une vallée de longueur finie qui débouche sur une plaine horizontale, et on postule, à l'interface air-sol, un flux thermique donné. On résout les équations du mouvement numériquement, et on obtient un écoulement où les vents de vallée (longitudinaux) et de pente (transversaux), leurs contre-vents respectifs, et des courants verticaux, sont les caractères principaux.

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With 12 Figures

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Contribution No. 98 of the Department of Atmospheric Sciences, University of Washington, Seattle, USA.     

Lidar and Sun photometer observations of atmospheric boundary-layer characteristics over an urban area in a mountain valley

We present measurements of the vertical aerosol structure and the aerosol optical depth in the lower troposphere performed above the city of Sofia (an urban area situated in a mountain valley), western Bulgaria by means of a ground-based aerosol lidar operating continuously for a number of years. The lidar measurements were accompanied by measurements of the aerosol optical depth (AOD) in the visible and near infrared regions of the spectrum performed in October 2004 using Microtops II radiometers. The maximum values of the AOD were found to occur 1–2 h before the complete development of the atmospheric boundary layer, i.e. during the residual layer destruction, which confirms our hypothesis concerning the slope circulation effect on the processes taking place in the atmospheric boundary layer. The AOD values obtained by the lidar are lower than those taken by the sun photometer. Further, the AOD exhibits two different types of behaviour. In the case of a ‘clear atmosphere’ (i.e. in the absence of volcanic eruptions and/or dust transport from the Sahara) most of the aerosol accumulated within the atmospheric boundary layer over the urban area considered. The combined use of the two instruments allows the comparison between the optical characteristics of the atmospheric aerosol (e.g. aerosol extinction coefficient, etc.) obtained by the lidar and through an independent method (sun photometer).     

A numerical simulation of boundary-layer flows near shelterbelts

We have developed a shelterbelt boundary-layer numerical model to study the patterns and dynamic processes relating to flow interaction with shelterbelts. The model simulates characteristics of all three zones of airflow passing over and through shelterbelts: the windward windspeed-reduction zone, the overspeeding zone above the shelterbelt, and the leeward windspeed-reduction zone. Locations of the maximum windspeed reduction and recirculation zone, as well as the leeward windspeed-recovery rate are well simulated by the model. Where comparisons with field measurements and wind-tunnel experiments were possible, the model demonstrated good performance for flows over and through shelters ranging from almost completely open to almost solid. The dynamic pressure resulting from the convergence and divergence of the flow field alters the perturbation pressure field. The disturbed pressure controls not only the formation of the separated flow but also the location of maximum windspeed reduction, streamline curvature, speed-up over the shelterbelt, and leeward windspeed recovery rate. The interaction of pressure with the flow produces complex flow patterns, the characteristics of which are determined, to a great extent, by shelterbelt structure.     

A numerical study of the effects of synoptic baroclinicity on stable boundary-layer evolution

The effects of synoptic baroclinicity on the evolution of the stable boundary layer are studied by using a numerical model in which the eddy exchange coefficients are determined from the turbulent kinetic energy and a local turbulent length scale. For model verification, several barotropic simulations are compared with those of higher-order closure models. The model predicts the existence of a value of geostrophic wind shear at which the nocturnal jet reaches its maximum intensity. The mechanism by which ageostrophic flow is generated and the role it plays in the development of the jet are explored. As baroclinicity increases, the directional shear in the wind near the level of the jet increases, thereby allowing the nocturnal inversion to grow to levels well above that of the jet.Journal Paper No. J-11109 of the Iowa Agriculture and Home Economics Experiment Station, Ames, IA. Project 2521.     

A planetary boundary-layer numerical model containing third-order derivative terms

In this paper, the third-order derivative of velocity with respect to height is included in the traditional motion equations of the neutral PBL. The nonlinear equations are solved numerically to obtain the vertical distribution of wind in the PBL and some PBL characteristic parameters. Reasonable simulations of the Leipzig wind profile using these parameters show the success of this kind of nonlocal closure in a real PBL simulation.     

A combined numerical and wind-tunnel study of ventilation and air pollution episodes in a rural valley of Switzerland

A study is reported of air pollution episodes in the Broye valley, a rural area of Switzerland located to the north-east of the city of Lausanne, in which a number of industrial sources of SO₂ are located. The study comprises numerical simulations of regional-scale meteorology, local plume behavior, as well as a wind tunnel investigation of the same region in order to ascertain the relative advantages and disadvantages of numerical and physical modeling. In situ data are available for certain episodes which occured during a very cold period in the winter of 1985, allowing intercomparisons to be made between nature and models. Furthermore, a significant effort undertaken by cantonal authorities has led to the setting up of a detailed emission inventory, which includes industry, individual domestic heating and traffic. Such an inventory has proved invaluable in imposing source terms in the models.     

Requirements for large-eddy simulation of surface wind gusts in a mountain valley

During the passage of a front, data from a light-weight cup anemometer and wind vane, sited in a steep-walled glacial valley of the Mt Cook region of the Southern Alps of New Zealand, were analysed to derive a power spectrum of the wind velocity for periods between 0.5 and 16 min. The energy spectrum roughly followed a -5/3 power law over the range of periods from 0.5–4 min — as might be expected in the case of an inertial subrange of eddies. However, any inertial subrange clearly does not extend to periods longer than this. We suggest that the observed eddies were generated in a turbulent wake associated with flow separation at the ridge crests, and large eddies are shed at periods of 4–8 min or more.A compressible fluid-dynamic model, with a Smagorinsky turbulence closure scheme and a law of the wall at the surface, was used to calculate flow over a cross section through this area in neutrally stratified conditions. A range of parameters was explored to assess some of the requirements for simulating surface wind gusts in mountainous terrain in New Zealand.In order to approximate the observed wind spectrum at Tasman aerodrome, Mount Cook, we found the model must be three-dimensional, with a horizontal resolution better than 250 m and with a Reynolds-stress eddy viscosity of less than 5 m² s^-1. In two-dimensional simulations, the eddies were too big in size and in amplitude and at the surface this was associated with reversed flow extending too far downstream. In contrast the three-dimensional simulations gave a realistic gusting effect associated with large scale cat's paws (a bigger variety of those commonly seen over water downstream of moderate hills), with reversed flow only at the steep part of the lee slope. The simulations were uniformly improved by better resolution, at all tested resolutions down to 250 m mesh size.The spectra of large eddies simulated in steep terrain were not very sensitive to the details of the eddy stress formulation. We suggest that this is because boundary-layer separation is forced in any case by terrain-induced pressure gradients.     

背风坡流场和浓度场的数值模拟

本文利用数值积分方法求解二维山地地形大气热力-动力学方程组以及扩散方程。模拟了山地背风坡的流场情况.作为应用,模拟了背风坡不同位置上的排放源在不同的大气稳定度条件下浓度场的分布情况,通过浓度场的垂直扩散方差σ_z~2和实测资料的比较表明:本模式能够反映不同地形和不同天气条件下的污染物质输送及扩散状况,因而有可能成为解决复杂地形上污染扩散的实用方法.     

Study on a boundary-layer numerical model with inclusion of heterogeneous multi-layer vegetation

On the basis of improving the algorithm of the mixing length in and above forest canopies, a PBL numerical model including the multi-layer, heterogeneous vegetation is developed. Simulations indicate that different treatments of mixing length can make a great difference in the wind field especially for dense forest, and results from the improved mixing length scheme are in better agreement with observations than those from the original scheme. It may be expected that the improved mixing length scheme can lead to more ra-tional turbulent transfer than the original one. From the sensitivity experiments, we obtain the characteris-tics of both wind and temperature profiles in and above plant canopies, e.g., during the daytime, a stable thermal stratification exists near the surface in the canopies, but a neutral or slightly unstable condition ap-pears above plant canopies, while at night the reverse situations occur; the increase of the temperature of the dense-forest case is less than that of the sparse-forest case; the windspeed is reduced within the canopy lay-er and the large wind shear occurs near the treetop, etc.     

Incorporation of planetary boundary-layer processes into numerical forecasting models

A study has been made of the evolution of the planetary boundary layer height (PBLH), the heat flux, and momentum flux using Clarke's Wangara data for a period of two days and two nights, 33/34–34/35. The observed Wangara data are considered as being an output of the first two internal levels of a general circulation model, at 1000 and 2000 m height. A time-dependent equation has been used to forecast, explicitly, the PBLH for both convectively unstable and stable periods. A comparison is made between observed and computed values whenever possible. In the unstable case, the Deardorff model (1974) has been used for the prediction of the unstable PBLH. Part of the stable case study involved a formulation of a time-dependent model for the prediction of the stable PBLH. The solution obtained from the model compared favourably with the results of a model suggested by Khakimov. Contribution number 382.     

Results from the MERKUR experiment: Mass budget and vertical motions in a large valley during mountain and valley wind

Summary Based on measurements made in March 1982 in the Inn valley during the MERKUR experiment, an attempt was made to compute the mass budget of a large alpine valley during periods of mountain and valley wind.The computations come from measurements of the alongvalley mass flux and assumptions on the fluxes in the slope layer and tributaries.Vertical motions in the valley's atmosphere have been evaluated from the mass budget computations. These motions, including the subsidence which compensates for daytime upslope winds and the subsidence which compensates for the valley wind flowing into tributaries during the day, are of great importance for the understanding of the thermal circulation.The results allow better estimation of vertical advection, which contributes to the budgets of momentum and energy.With 8 Figures     

A study of wind speed modification and internal boundary-layer heights in a coastal region

Wind profile data within the first two kilometres of a coast have been used to study the wind field modification downstream of this surface discontinuity. The land area is generally very flat, having an overall roughness length of 0.04 m. A wind model, suitable for practical applications and inexpensive to run, has been tested against the data and was found to give satisfactory results. Knowing the climatological statistics of wind and stratification, e.g., at the coast, the model may thus be used to estimate, on a climatological basis, how the wind field is modified with distance inland, at least in areas with only minor topography. This type of information is of great importance when locating wind turbines. It is in these cases also important to know the statistics of the internal boundary-layer (IBL) height, as the turbulence intensity may be quite different in and above the IBL, which in turn may influence load and fatigue calculations. Using the wind profile data, the IBL height was clearly discernible in the majority of cases. Having very unstable stratification over land, the IBL height could, however, not be determined from the wind profiles, as the wind in these cases did not decrease inland. This result was also obtained using the wind model. A simple model of the type z _IBL = a · x ^b, was instead tested, and was shown to give reasonable results.     

Modifications of the structure of cold fronts over the foreland and in a mountain valley

Summary The investigations during the German Frontal Experiment 1987 show the modification of structure and movement of cold fronts in the vicinity of the Alps and in an Alpine valley. The two cold fronts that moved nearly parallel to the mountains were modified at the mountain barrier by the channelling effect. In those cases the postfrontal air flowed into the Inn valley from the valley's exit up-valley. The upper and lower parts of the fronts became detached, and the structure of the lower part changes on its way from the foreland to the mountain barrier.In contrast the fourth cold front, which moved from north-west to south-east, crossed the mountains without appreciable deformation although it suffered some degree of blocking and retardation.With 7 Figures     

A planetary boundary-layer study in the Mackenzie Valley,Canada

Detailed wind velocity profiles were obtained by means of a rocket-sonde technique to a height of about 700 m at a site in the Canadian Northwest Territories. Less detailed temperature observations were also made using a balloon sonde. The site was some 100 km east of the easternmost range of the Rocky Mountains. The observations took place in mid-February when the overall atmospheric static stability was considerable. The results showed the presence of an arctic, atmospheric ‘thermocline’ some 500 m above ground, which sloped up or down considerably, with the generators of isothermal surfaces usually parallel to the nearby mountains, in the manner of upwelled or downwelled thermoclines in the ocean near shore. There was often strong baroclinic flow parallel to the mountain range. Noticeable frictional effects were confined to a near-ground layer always less than 100 m and mostly no more than 10 m in height. An Ekman-type boundary layer could only be identified in about one-third of the velocity profiles. The non-dimensionalized depth coefficient of such layers was close to 0.1, the geostrophic drag coefficient about 2.5×10^?4.     

Some numerical studies of surface boundary-layer flow above gentle topography

A numerical model of two-dimensional surface boundary-layer flow based on a non orthogonal coordinate mapping is developed. Results show good agreement with previous computations using conformal mapping techniques for flow over a periodic wavy surface and over an isolated hill. Results are presented for flow over Gaussian hills and valleys and over smooth sloping escarpments. For a 1 in 4 Sine ramp, good agreement is obtained with Freeston's (1974) wind-tunnel measurements.Presented under the title Atmospheric boundary-layer flow above gentle topography at the 10th Annual Congress of the Canadian Meteorological Society, Quebec City, May 26–28, 1976.     

Numerical model simulations of boundary-layer dynamics during winter conditions

Summary  A mesoscale numerical model, incorporating a land-surface scheme based on Deardorffs’ approach, is used to study the diurnal variation of the boundary layer structure and surface fluxes during four consecutive days with air temperatures well below zero, snow covered ground and changing synoptic forcing. Model results are evaluated against in-situ measurements performed during the WINTEX field campaign held in Sodankyl?, Northern Finland in March 1997. The results show that the land-surface parameterization employed in the mesoscale model is not able to reproduce the magnitude of the daytime sensible heat fluxes and especially the pronounced maximum observed in the afternoon. Additional model simulations indicate that this drawback is to a large extent removed by the implementation of a shading factor in the original Deardorff scheme. The shading factor, as discussed in Gryning et al. (2001), accounts for the fact that in areas with sparse vegetation and low solar angles, both typical for the northern boreal forests in wintertime, absorption of direct solar radiation is due to an apparent vegetation cover which is much greater than the actual one (defined as the portion of the ground covered by vegetation projected vertically). Moreover, the observed asymmetry in the diurnal variation of the sensible heat flux indicates that there might be a significant heat storage in the vegetation. The implementation of an objective heat storage scheme in the mesoscale model explains part of the observed diurnal variation of the sensible heat flux. Received November 12, 1999 Revised October 4, 2000